A boundary layer problem arising in gravity-driven laminar film flow of power-law fluids along vertical walls

Original paper

Abstract.

A rigorous mathematical analysis is given for a boundary layer problem for a third-order nonlinear ordinary differential equation, which arises in gravity-driven laminar film flow of power-law fluids along vertical walls. Firstly, the problem is transformed into a singular nonlinear two-point boundary value problem of second order. Next, the latter is proved to have a unique positive solution, for which some estimates are established. Finally, the result above-mentioned is turned over to the original problem. The conclusion of this paper is that the boundary layer problem has a unique normal solution if the power-law index is less than or equal to one and a generalized normal solution if the power-law index is greater than one. Also the asymptotic behavior of the normal solution at the infinity is displayed.

Mathematics Subject Classification (2000).

76A05 76D10 34B15 

Keywords.

Boundary layer problem power-law index (generalized) normal solution singular nonlinear two-point boundary value problem positive solution existence uniqueness 

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Copyright information

© Birkhäuser Verlag, Basel 2004

Authors and Affiliations

  1. 1.Department of MathematicsXiamen UniversityXiamenPeople’s Republic of China
  2. 2.Department of MathematicsJilin UniversityChangchunPeople’s Republic of China

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